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Given a set of inelastic material models, a microstructure, a macroscopicstructural geometry, and a set of boundary conditions, one can in principlealways solve the governing equations to determine the system's mechanicalresponse. However, for large systems this procedure can quickly becomecomputationally overwhelming, especially in three-dimensions when themicrostructure is locally complex. In such settings multi-scale modeling offersa route to a more efficient model by holding out the promise of a frameworkwith fewer degrees of freedom, which at the same time faithfully represents, upto a certain scale, the behavior of the system.  In this paper, we present a methodology that produces such models forinelastic systems upon the basis of a variational scheme. The essence of thescheme is the construction of a variational statement for the free energy aswell as the dissipation potential for a coarse scale model in terms of the freeenergy and dissipation functions of the fine scale model. From the coarse scaleenergy and dissipation we can then generate coarse scale material models thatare computationally far more efficient than either directly solving the finescale model or by resorting to FE-square type modeling. Moreover, the coarsescale model preserves the essential mathematical structure of the fine scalemodel.  An essential feature for such schemes is the proper definition of the coarsescale inelastic variables. By way of concrete examples, we illustrate theneeded steps to generate successful models via application to problems inclassical plasticity, included are comparisons to direct numerical simulationsof the microstructure to illustrate the accuracy of the proposed methodology.

A variational approach to effective models for inelastic systems